East london is definitely one of the most creative spots in London, if not even in England or the world. It’s a nucleus for recent music developments like Garage, Grime and urban music in general: (here is a great BBC 1Xtra documentary about London’s east end music, and there’s even an East London Blog).
East London consists of neighbourhoods like Hackney, Shoreditch, Whitechapel, Bow, Bethnal Green and so on. Especially the latter is famous for its galleries, e.g. One in the other where the McNally exhib was at. All in former industrial buildings, hidden in basements and behind metal curtains, focusing on young and raw artists, more the art of tomorrow than the art of today one finds in random and commercial central London galleries.
Every first thursday in a month, there is an event, that holds the whole scene together: firstthursdays – Late night art in East London. Over 80 galleries and museums open until 9pm. So, it is like: Tomorrow! If I’d still be in London I’d definitely check it out.